If you want to use a single video output to send 3 different images to 3 different projectors, the only device I'm aware of which will do that -- and this *is* my gig -- is the Matrox Triple-Head-To-Go, which makes your video output look like a 5760x1080 monitor, and then splits it to three outputs.
Alternatively, you'll need three separate DisplayLink adapters, one per channel, and *either way*, you will need 3 separate HDbaseT media converters -- every step of this process is sui generis enough that you will *not* find one box that does everything. And maybe you'll be able to run all three DisplayLink adapters, and maybe not; I've never tried it.
Sorry about that.
The Trashcan Mac, as you probably realize, *will* drive all three projectors, plus a control monitor, directly, if you have it cabled properly. You might want to critically re-evaluate "outgrew"...